Face-up Size

All things being equal, Diamond will face-up smaller than Amethyst for a given
carat weight, because it has higher specific gravity
(3.52 vs. 2.65 - this means it's "heavier" compared to Amethyst of the same size). Face-up size also depends heavily on the
proportions of the cut.

Face-up area is a measure of the size of the gem when viewed from above (as set in a ring).
It tells you how big the gem is at the girdle plane.